To compute [tex]\(\log_7{98}\)[/tex], we need to determine the power to which the base 7 must be raised to produce 98.
In simpler terms, we are looking for [tex]\(x\)[/tex] in the equation:
[tex]\[ 7^x = 98 \][/tex]
Since logarithms are the inverse operations of exponentiation, we can express [tex]\(x\)[/tex] using the logarithm:
[tex]\[ x = \log_7{98} \][/tex]
After solving this logarithm, we find:
[tex]\[ \log_7{98} \approx 2.3562071871080223 \][/tex]
So, the value of [tex]\(\log_7{98}\)[/tex] is approximately [tex]\(2.3562071871080223\)[/tex].
